Definition of Rainfall Thresholds for Landslides Using Unbalanced Datasets: Two Case Studies in Shaanxi Province, China
Abstract
1. Introduction
2. Materials and Methods
2.1. Study Area
2.2. Datasets
2.3. Methods
2.3.1. Reconstruction of Rainfall Events
2.3.2. Definition of Rainfall Thresholds
- Efficiency index (Equation (2));
- True positive rate (also referred to as hit rate, probability of detection rate, and sensitivity (Equation (3)));
- False positive rate (also referred to as probability of false detection (Equation (4)));
- Positive predictive value (also referred to as precision (Equation (5)));
3. Results
3.1. Reconstraction of Rainfall Events
3.2. Definition of Rainfall Thresholds
3.3. Performance Evaluation
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter Name | Parameter Value | Unit | |
---|---|---|---|
Warm Periods (CW) | Cold Periods (CC) | ||
Gs | 0.1 | 0.1 | mm |
ER | 0.2 | 0.2 | mm |
Rb | 15 | 15 | km |
P1 | 3 | 6 | h |
P2 | 6 | 12 | h |
P3 | 1 | 1 | mm |
P4 | 48 | 96 | h |
Actual Events | |||
---|---|---|---|
Landslides | No Landslides | ||
Predicted events | Landslides: E ≥ f(D) | TP | FP |
No landslides: E < f(D) | FN | TN |
Events | Number | Duration (h) | Cumulated Rainfall (mm) | ||
---|---|---|---|---|---|
Min | Max | Min | Max | ||
LY | |||||
RE | 2467 | 1 | 1075 | 1.1 | 690 |
RE associated with landslides | 29 | 2 | 383 | 14.5 | 690 |
MRC total/not considering repetitions | 465/233 | 2 | 230 | 5.1 | 306.8 |
MPRC total/not considering repetitions | 171/74 | 2 | 120 | 5.3 | 277.9 |
Non-triggering RE | 2438 | 1 | 1075 | 1.1 | 381.9 |
XY | |||||
RE | 3229 | 1 | 669 | 1.1 | 298 |
RE associated with landslides | 19 | 13 | 669 | 21 | 298 |
MRC | 45 | 3 | 337 | 7.9 | 163.9 |
MPRC | 21 | 3 | 187 | 13.3 | 163.9 |
Non-triggering RE | 3210 | 1 | 526 | 1.1 | 280 |
Label | Threshold Equation | △α/α (%) | △γ/γ (%) |
---|---|---|---|
N5,LY | E = (10.44 ± 0.45) × D(0.57 ± 0.01) | 4% | 2% |
N10,LY | E = (7.43 ± 0.31) × D(0.57 ± 0.01) | 4% | 2% |
N15,LY | E = (5.91 ± 0.24) × D(0.57 ± 0.01) | 4% | 2% |
N20,LY | E = (4.92 ± 0.20) × D(0.57 ± 0.01) | 4% | 2% |
N50,LY | E = (2.24 ± 0.09) × D(0.57 ± 0.01) | 4% | 2% |
N5,XY | E = (10.78 ± 0.40) × D(0.57 ± 0.01) | 4% | 2% |
N10,XY | E = (7.91 ± 0.29) × D(0.57 ± 0.01) | 4% | 2% |
N15,XY | E = (6.42 ± 0.22) × D(0.57 ± 0.01) | 3% | 2% |
N20,XY | E = (5.43 ± 0.19) × D(0.57 ± 0.01) | 3% | 2% |
N50,XY | E = (2.65 ± 0.08) × D(0.57 ± 0.01) | 3% | 2% |
Label | Threshold Equation | △α/α (%) | △γ/γ (%) |
---|---|---|---|
P20,LY,MRC | E = (14.59 ± 1.93) × D(0.38 ± 0.03) | 13% | 8% |
P15,LY,MRC | E = (13.61 ± 1.84) × D(0.38 ± 0.03) | 14% | 8% |
P10,LY,MRC | E = (12.48 ± 1.74) × D(0.38 ± 0.03) | 14% | 8% |
P5,LY,MRC | E = (10.97 ± 1.59) × D(0.38 ± 0.03) | 14% | 8% |
P50,LY,MRC | E = (19.68 ± 2.35) × D(0.38 ± 0.03) | 12% | 8% |
P20,XY,MRC | E = (10.98 ± 5.60) × D(0.34 ± 0.10) | 51% | 28% |
P15,XY,MRC | E = (10.12 ± 5.19) × D(0.34 ± 0.10) | 51% | 28% |
P10,XY,MRC | E = (8.98 ± 4.53) × D(0.34 ± 0.10) | 50% | 28% |
P5,XY,MRC | E = (7.61 ± 3.81) × D(0.34 ± 0.10) | 50% | 28% |
P50,XY,MRC | E = (16.13 ± 8.41) × D(0.34 ± 0.10) | 52% | 28% |
P20,LY,MPRC | E = (11.80 ± 2.14) × D(0.47 ± 0.05) | 18% | 12% |
P15,LY,MPRC | E = (10.73 ± 1.99) × D(0.47 ± 0.05) | 19% | 12% |
P10,LY,MPRC | E = (9.51 ± 1.82) × D(0.47 ± 0.05) | 19% | 12% |
P5,LY,MPRC | E = (7.96 ± 1.58) × D(0.47 ± 0.05) | 20% | 12% |
P50,LY,MPRC | E = (17.84 ± 2.92) × D(0.47 ± 0.05) | 16% | 12% |
P20,XY,MPRC | E = (24.43 ± 19.85) × D(0.18 ± 0.17) | 81% | 96% |
P15,XY,MPRC | E = (22.04 ± 17.58) × D(0.18 ± 0.17) | 80% | 96% |
P10,XY,MPRC | E = (19.36 ± 14.91) × D(0.18 ± 0.17) | 77% | 96% |
P5,XY,MPRC | E = (15.99 ± 11.92) × D(0.18 ± 0.17) | 75% | 96% |
P50,XY,MPRC | E = (38.10 ± 33.51) × D(0.18 ± 0.17) | 88% | 96% |
Label | TP | FN | FP | TN |
---|---|---|---|---|
N5,LY | 54 | 20 | 16 | 543 |
N10,LY | 65 | 9 | 37 | 522 |
N15,LY | 70 | 4 | 60 | 499 |
N20,LY | 71 | 3 | 92 | 467 |
P20,LY,MRC | 62 | 12 | 41 | 518 |
P15,LY,MRC | 65 | 9 | 44 | 515 |
P10,LY,MRC | 67 | 7 | 54 | 505 |
P5,LY,MRC | 68 | 6 | 64 | 495 |
P20,LY,MPRC | 62 | 12 | 29 | 530 |
P15,LY,MPRC | 63 | 11 | 34 | 525 |
P10,LY,MPRC | 66 | 8 | 48 | 511 |
P5,LY,MPRC | 70 | 4 | 61 | 498 |
Label | TP | FN | FP | TN |
---|---|---|---|---|
N5,XY | 4 | 17 | 33 | 885 |
N10,XY | 7 | 14 | 103 | 815 |
N15,XY | 14 | 7 | 146 | 772 |
N20,XY | 17 | 4 | 184 | 734 |
P20,XY,MRC | 17 | 4 | 210 | 708 |
P15,XY,MRC | 17 | 4 | 223 | 695 |
P10,XY,MRC | 18 | 3 | 258 | 660 |
P5,XY,MRC | 19 | 2 | 279 | 639 |
P20,XY,MPRC | 15 | 6 | 171 | 747 |
P15,XY,MPRC | 17 | 4 | 190 | 728 |
P10,XY,MPRC | 17 | 4 | 214 | 704 |
P5,XY,MPRC | 18 | 3 | 255 | 663 |
Label | EI | TPR | FPR | PPV | δ |
---|---|---|---|---|---|
N5,LY | 0.94 | 0.73 | 0.03 | 0.77 | 0.271 |
N10,LY | 0.93 | 0.88 | 0.07 | 0.64 | 0.134 |
N15,LY | 0.90 | 0.95 | 0.11 | 0.54 | 0.121 |
N20,LY | 0.85 | 0.96 | 0.16 | 0.44 | 0.165 |
P20,LY,MRC | 0.92 | 0.84 | 0.07 | 0.60 | 0.175 |
P15,LY,MRC | 0.92 | 0.88 | 0.08 | 0.60 | 0.411 |
P10,LY,MRC | 0.90 | 0.91 | 0.10 | 0.55 | 0.135 |
P5,LY,MRC | 0.89 | 0.92 | 0.11 | 0.52 | 0.136 |
P20,LY,MPRC | 0.94 | 0.84 | 0.05 | 0.68 | 0.168 |
P15,LY,MPRC | 0.93 | 0.85 | 0.06 | 0.65 | 0.162 |
P10,LY,MPRC | 0.91 | 0.89 | 0.09 | 0.58 | 0.142 |
P5,LY,MPRC | 0.90 | 0.95 | 0.11 | 0.53 | 0.121 |
Label | EI | TPR | FPR | PPV | δ |
---|---|---|---|---|---|
N5,XY | 0.95 | 0.19 | 0.04 | 0.11 | 0.811 |
N10,XY | 0.88 | 0.33 | 0.11 | 0.06 | 0.679 |
N15,XY | 0.84 | 0.71 | 0.16 | 0.09 | 0.331 |
N20,XY | 0.80 | 0.81 | 0.20 | 0.08 | 0.276 |
P20,XY,MRC | 0.77 | 0.81 | 0.23 | 0.07 | 0.298 |
P15,XY,MRC | 0.76 | 0.81 | 0.24 | 0.07 | 0.306 |
P10,XY,MRC | 0.72 | 0.86 | 0.28 | 0.07 | 0.313 |
P5,XY,MRC | 0.70 | 0.90 | 0.30 | 0.06 | 0.316 |
P20,XY,MPRC | 0.81 | 0.71 | 0.19 | 0.08 | 0.347 |
P15,XY,MPRC | 0.79 | 0.81 | 0.21 | 0.08 | 0.283 |
P10,XY,MPRC | 0.77 | 0.81 | 0.23 | 0.07 | 0.298 |
P5,XY,MPRC | 0.73 | 0.86 | 0.28 | 0.07 | 0.313 |
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Zhang, S.; Pecoraro, G.; Jiang, Q.; Calvello, M. Definition of Rainfall Thresholds for Landslides Using Unbalanced Datasets: Two Case Studies in Shaanxi Province, China. Water 2023, 15, 1058. https://doi.org/10.3390/w15061058
Zhang S, Pecoraro G, Jiang Q, Calvello M. Definition of Rainfall Thresholds for Landslides Using Unbalanced Datasets: Two Case Studies in Shaanxi Province, China. Water. 2023; 15(6):1058. https://doi.org/10.3390/w15061058
Chicago/Turabian StyleZhang, Sen, Gaetano Pecoraro, Qigang Jiang, and Michele Calvello. 2023. "Definition of Rainfall Thresholds for Landslides Using Unbalanced Datasets: Two Case Studies in Shaanxi Province, China" Water 15, no. 6: 1058. https://doi.org/10.3390/w15061058
APA StyleZhang, S., Pecoraro, G., Jiang, Q., & Calvello, M. (2023). Definition of Rainfall Thresholds for Landslides Using Unbalanced Datasets: Two Case Studies in Shaanxi Province, China. Water, 15(6), 1058. https://doi.org/10.3390/w15061058